The CAP theorem asserts a trilemma between consistency, availability, and partition tolerance. This paper introduces a rigorous automata-theoretic and economically grounded framework that reframes the CAP trade-off as a constraint optimization problem. We model distributed systems as partition-aware state machines and embed economic incentive layers to stabilize consensus behavior across adversarially partitioned networks. By incorporating game-theoretic mechanisms into the global transition semantics, we define provable bounds on convergence, liveness, and correctness. Our results demonstrate that availability and consistency can be simultaneously preserved within bounded epsilon margins, effectively extending the classical CAP limits through formal economic control.
Randomized fault-tolerant consensus protocols with common coins are widely used in cloud computing and blockchain platforms. Due to their fundamental role, it is vital to guarantee their correctness. Threshold automata is a formal model designed for the verification of fault-tolerant consensus protocols. It has recently been extended to probabilistic threshold automata (PTAs) to verify randomized fault-tolerant consensus protocols. Nevertheless, PTA can only model randomized consensus protocols with local coins. In this work, we extend PTA to verify randomized fault-tolerant consensus protocols with common coins. Our main idea is to add a process to simulate the common coin (the so-called common-coin process). Although the addition of the common-coin process destroys the symmetry and poses technical challenges, we show how PTA can be adapted to overcome the challenges. We apply our approach to verify the agreement, validity and almost-sure termination properties of 8 randomized consensus protocols with common coins.
The communities of blockchains and distributed ledgers have been stirred up by the introduction of zero-knowledge proofs (ZKPs). Originally designed to solve privacy issues, ZKPs have now evolved into an effective remedy for scalability concerns and are applied in Zcash (internet money like Bitcoin). To enable ZKPs, Rank-1 Constraint Systems (R1CS) offer a verifier for bi-linear equations. To accurately and efficiently represent R1CS, several language tools like Circom, Noir, and Snarky have been proposed to automate the compilation of advanced programs into R1CS. However, due to the flexible nature of R1CS representation, there can be significant differences in the compiled R1CS forms generated from circuit language programs with the same underlying semantics. To address this issue, this paper uses a data-flow-based R1CS paradigm algorithm, which produces a standardized format for different R1CS instances with identical semantics. By using the normalized R1CS format circuits, the complexity of circuits' verification can be reduced. In addition, this paper presents an R1CS normalization algorithm benchmark, and our experimental evaluation demonstrates the effectiveness and correctness of our methods.
Mojtaba Eshghie, Wolfgang Ahrendt, Cyrille Artho, Thomas Hildebrandt · 5 authors
Smart contracts manage blockchain assets and embody business processes. However, mainstream smart contract programming languages such as Solidity lack explicit notions of roles, action dependencies, and time. Instead, these concepts are implemented in program code. This makes it very hard to design and analyze smart contracts. We argue that DCR graphs are a suitable formalization tool for smart contracts because they explicitly and visually capture the mentioned features. We utilize this expressiveness to show that many common high-level design patterns representing the underlying business processes in smart contract applications can be naturally modeled this way. Applying these patterns shows that DCR graphs facilitate the development and analysis of correct and reliable smart contracts by providing a clear and easy-to-understand specification.
Pedro D. Manrique, Frank Huo, Sara El Oud, Minzhang Zheng · 6 authors
Online communities featuring 'anti-X' hate and extremism, somehow thrive online despite moderator pressure. We present a first-principles theory of their dynamics, which accounts for the fact that the online population comprises diverse individuals and evolves in time. The resulting equation represents a novel generalization of nonlinear fluid physics and explains the observed behavior across scales. Its shockwave-like solutions explain how, why and when such activity rises from 'out-of-nowhere', and show how it can be delayed, re-shaped and even prevented by adjusting the online collective chemistry. This theory and findings should also be applicable to anti-X activity in next-generation ecosystems featuring blockchain platforms and Metaverses.
Nathalie Bertrand, Vincent Gramoli, Igor Konnov, Marijana Lazić · 6 authors
Blockchain has recently attracted the attention of the industry due, in part, to its ability to automate asset transfers. It requires distributed participants to reach a consensus on a block despite the presence of malicious (a.k.a. Byzantine) participants. Malicious participants exploit regularly weaknesses of these blockchain consensus algorithms, with sometimes devastating consequences. In fact, these weaknesses are quite common and are well illustrated by the flaws in the hand-written proofs of existing blockchain consensus protocols [63]. Paradoxically, until now, no blockchain consensus has been holistically verified using model checking. In this paper, we remedy this paradox by model checking for the first time a blockchain consensus used in industry. We propose a holistic approach to verify the consensus algorithm of the Red Belly Blockchain [20], for any number $n$ of processes and any number $f<n/3$ of Byzantine processes. We decompose directly the algorithm pseudocode in two parts -- an inner broadcast algorithm and an outer decision algorithm -- each modelled as a threshold automaton [36], and we formalize their expected properties in linear-time temporal logic. We then automatically check the inner broadcasting algorithm, under a carefully identified fairness assumption. For the verification of the outer algorithm, we simplify the model of the inner algorithm by relying on its checked properties. Doing so, we formally verify not only the safety properties of the Red Belly Blockchain consensus but also its liveness in about 70 seconds.
Transactions involving multiple blockchains are implemented by cross-chain protocols. These protocols are based on smart contracts, programs that run on blockchains, executed by a network of computers. Because smart contracts can automatically transfer ownership of cryptocurrencies, electronic securities, and other valuable assets among untrusting parties, verifying the runtime correctness of smart contracts is a problem of compelling practical interest. Such verification is challenging since smart contract execution is time-sensitive, and the clocks on different blockchains may not be perfectly synchronized. This paper describes a method for runtime monitoring of blockchain executions. First, we propose a generalized runtime verification technique for verifying partially synchronous distributed computations for the metric temporal logic (MTL) by exploiting bounded-skew clock synchronization. Second, we introduce a progression-based formula rewriting scheme for monitoring \MTL specifications which employ SMT solving techniques and report experimental results.
We present a novel mathematical framework for the specification and analysis of fault-resilient distributed protocols and their implementations, with the following components: 1. Transition systems that allow the specification and analysis of computations with safety and liveness faults and their fault resilience. 2. Notions of safe, live and complete implementations among transition systems and their composition, with which the correctness (safety and liveness) and completeness of a protocol stack as a whole follows from each protocol implementing correctly and completely the protocol above it in the stack. 3. Applying the notion of monotonicity, pertinent to histories of distributed computing systems, to ease the specification and proof of correctness of implementations among distributed computing systems. 4. Multiagent transition systems, further characterized as centralized/distributed and synchronous/asynchronous; safety and liveness fault-resilience of implementations among them and their composition. The framework is being employed in the specification of a grassroots ordering consensus protocol stack, with a grassroots dissemination protocol and its implementation of grassroots social networking and of sovereign cryptocurrencies, and an efficient Byzantine atomic broadcast protocols as initial applications.
Paolo Modesti, Siamak F. Shahandashti, Patrick McCorry, Feng Hao
The Payment Protocol standard BIP70, specifying how payments in Bitcoin are performed by merchants and customers, is supported by the largest payment processors and most widely-used wallets. The protocol has been shown to be vulnerable to refund attacks due to lack of authentication of the refund addresses. In this paper, we give the first formal model of the protocol and formalise the refund address security goals for the protocol, namely refund address authentication and secrecy. The formal model utilises communication channels as abstractions conveying security goals on which the protocol modeller and verifier can rely. We analyse the Payment Protocol confirming that it is vulnerable to an attack violating the refund address authentication security goal. Moreover, we present a concrete protocol revision proposal supporting the merchant with publicly verifiable evidence that can mitigate the attack. We verify that the revised protocol meets the security goals defined for the refund address. Hence, we demonstrate that the revised protocol is secure, not only against the existing attacks, but also against any further attacks violating the formalised security goals.
Fabrizio Romano Genovese, Jelle Herold, Fosco Loregian, Daniele Palombi
We show how a particular variety of hierarchical nets, where the firing of a transition in the parent net must correspond to an execution in some child net, can be modelled utilizing a functorial semantics from a free category -- representing the parent net -- to the category of sets and spans between them. This semantics can be internalized via Grothendieck construction, resulting in the category of executions of a Petri net representing the semantics of the overall hierarchical net. We conclude the paper by giving an engineering-oriented overview of how our model of hierarchical nets can be implemented in a transaction-based smart contract environment.
Massimo Bartoletti, James Hsin-yu Chiang, Alberto Lluch Lafuente
Automated market makers (AMMs) are one of the most prominent decentralized finance (DeFi) applications. AMMs allow users to trade different types of crypto-tokens, without the need to find a counter-party. There are several implementations and models for AMMs, featuring a variety of sophisticated economic mechanisms. We present a theory of AMMs. The core of our theory is an abstract operational model of the interactions between users and AMMs, which can be concretised by instantiating the economic mechanisms. We exploit our theory to formally prove a set of fundamental properties of AMMs, characterizing both structural and economic aspects. We do this by abstracting from the actual economic mechanisms used in implementations, and identifying sufficient conditions which ensure the relevant properties. Notably, we devise a general solution to the arbitrage problem, the main game-theoretic foundation behind the economic mechanisms of AMMs.
Blockchain-based distributed computing platforms enable the trusted execution of computation - defined in the form of smart contracts - without trusted agents. Smart contracts are envisioned to have a variety of applications, ranging from financial to IoT asset tracking. Unfortunately, the development of smart contracts has proven to be extremely error prone. In practice, contracts are riddled with security vulnerabilities comprising a critical issue since bugs are by design non-fixable and contracts may handle financial assets of significant value. To facilitate the development of secure smart contracts, we have created the FSolidM framework, which allows developers to define contracts as finite state machines (FSMs) with rigorous and clear semantics. FSolidM provides an easy-to-use graphical editor for specifying FSMs, a code generator for creating Ethereum smart contracts, and a set of plugins that developers may add to their FSMs to enhance security and functionality.
The adoption of blockchain-based distributed computation platforms is growing fast. Some of these platforms, such as Ethereum, provide support for implementing smart contracts, which are envisioned to have novel applications in a broad range of areas, including finance and Internet-of-Things. However, a significant number of smart contracts deployed in practice suffer from security vulnerabilities, which enable malicious users to steal assets from a contract or to cause damage. Vulnerabilities present a serious issue since contracts may handle financial assets of considerable value, and contract bugs are non-fixable by design. To help developers create more secure smart contracts, we introduce FSolidM, a framework rooted in rigorous semantics for designing con- tracts as Finite State Machines (FSM). We present a tool for creating FSM on an easy-to-use graphical interface and for automatically generating Ethereum contracts. Further, we introduce a set of design patterns, which we implement as plugins that developers can easily add to their contracts to enhance security and functionality.